Question: A B C If: $ AB = 9x + 9$, $ AC = 31$, and $ BC = 7x + 6$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 9} + {7x + 6} = {31}$ Combine like terms: $ 16x + 15 = {31}$ Subtract $15$ from both sides: $ 16x = 16$ Divide both sides by $16$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $BC$ $ BC = 7({1}) + 6$ Simplify: $ {BC = 7 + 6}$ Simplify to find ${BC}$ : $ {BC = 13}$